Question

a jar contains 5 red marbles, numbered 1 to 5, and 11 blue marbles numbered 1 to 11. a marble is chosen at random. give answer as a fraction.
a) if youre told the marble is red, what is the probability that it has the number 3 on it?
b) if youre told the marble has the number 9 on it, what is the probability the marble is red?

Explanation:

Step1: Calculate probability for part a

There are 5 red marbles and only 1 red marble has the number 3. The probability of an event is the number of favorable outcomes divided by the number of total outcomes. Given the marble is red, the total number of red - marbles is the total outcomes and the number of red marbles with number 3 is the favorable outcome.
$P(\text{number 3}|\text{red})=\frac{1}{5}$

Step2: Calculate probability for part b

There is 0 red marble with the number 9 and 1 blue marble with the number 9. The total number of marbles with the number 9 is 1.
$P(\text{red}|\text{number 9}) = 0$

Answer:

a) $\frac{1}{5}$
b) $0$